A new infinite-dimensional Linking theorem with application to a system of coupled Poisson equations

TL;DR

This paper introduces a new infinite-dimensional linking theorem for strongly indefinite functionals using the $ au$-topology, and applies it to prove the existence of solutions for coupled Poisson equations.

Contribution

It generalizes the classical linking theorem to infinite-dimensional settings with strongly indefinite functionals using $ au$-topology.

Findings

Established a new linking theorem for strongly indefinite functionals.

Proved the existence of nontrivial solutions for a system of coupled Poisson equations.

Abstract

Using the minimax technique from the critical point theory, which consists in constructing or transforming a suitable class of applications such that a critical value $c$ of a functional $f$ can be characterized as a minimax value over this class, we establish a new natural infinite-dimensional linking theorem for strongly indefinite functionals by using the $\tau-$topology of Kryszewski and Szulkin. Our result is a generalization of the classical linking theorem \cite[Theorem 2.21]{Wi}. As an application, we obtain the existence of a nontrivial solution to a system of coupled Poisson equations.